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Statistical Analysis of Signaling

Carlos Bouza (Université La Havane, Cuba),bouza@matcom.uh.cu

Résumé : The use of signals for modelling different problems is common in economics and biometry. We will discuss how statistical approaches work in the de-codification. The usual approach is to consider the structure of a game. The decisions of the decision maker are to provide a classification. The evaluation of the posterior probability of classifying correctly provides a decision rule. We consider the use of a naïve estimator, based on a density function estimator. Neural Networks models considered as another method for coping with the classification. We consider the problem of Labour Market (Analysis of Labor Market Signaling using the probability of misclassification and neural networks Carlos N. Bouza Herrera, Josefina Martínez Barbeito and Pasha G. Mitra, to be published by Mat. E Estat. , S. Paulo) . A discussion of the use of this approach in the classification of fingers print (a research in development) is developed. Monte Carlo experiments are used for evaluating the behaviour of the proposals. Though many financial models deal with concepts that are linked to regression their unpopularity is common in practice. A key example is that of the study of the risk-adjusted return of the portfolio. The general equation is regarded as r - Rf = + ( Km - Rf ), where r is the fund’s return rate, Rf is the risk-free return rate, and Km is the return of the index. This can be regarded as the usual equation for CAPM excepting the existence of . is the ´beta´ derived from the classic Sharpe’s representation of equilibrium prices. When fitting a regression we include an error term and represents how much better the fund did than the predicted CAPM, (Prediction of CAPM and robust regression models

Carlos N. Bouza Herrera, Sira Allende Alonso, Daniel C. Chen and Josefina Martinez Barbeito, VIII Paraopt, Cairo, Egypt, November 2005, Estimating Beta in Capital Asset Pricing Modeling : The Use of a Combination of OLS and LAD, 4ª Conferencia Iberoamericana en Sistemas, Cibernética e Informática (CISCI 2005), july de 2005, Orlando, Florida, EE.UU.). We revise this problem considering that the residuals are distributed according to Stable distributions, not necessarily a normal. Some related financial problems are considered in a similar fashion. Monte Carlo experiments are developed for comparing different methods for estimating the so-called beta-coefficients.